Looking out for Tactics

1) When you first scan a board, looking for tactics, what do you look for first? and 2nd? etc. Do you first look for big pieces lined up for possible pins/skewers? Or do you look for hanging/loose pieces? Or possible forks? Holes? Weak/open King position? Other things? Lastly, for sacs? What order and what do you look for?

Very generally what you really want to find are moves that both have a threat and have a limited number of responses. It may be a queen sac and look crazy at first, but if there is a threat (they can't ignore it), and if they can only respond 1 or 2 ways, then it's a move worth looking at every time. Some features that help find these forcing moves are undefended (or loose) pieces and/or an exposed enemy king.

In a tactical puzzle, and if I'm not warmed up yet, I'll look at the lines of force (so to speak) each piece exerts, even if it's through other pieces. So a bishop on c3 I'll trace the c3-h8 diagonal with my eyes. This way in future calculations I'll know without having to look that each piece removed from that diagonal is freeing that bishop. Of course pattern recognition helps a lot. So yeah, things like pieces lined up on a line or if they're forkable. As you calculate you may notice some key squares too, and you start to notice when those squares are lined up or forkable as well which can lead to solutions.

If I'm having trouble solving it, I remind myself each move must have a threat associated with it. For example I try to avoid just looking at a random sacrifice like rook takes pawn. What makes the move wroth exploring (as mentioned above) is that they can't ignore it, and they can only respond to it in a few ways.

The scanning before any calculation just takes a few seconds. At that point usually a few ideas already suggest themselves and it's time to calculate.

the first you need to look is the material, always count it and the reason is simple, if you are down something like a queen probably you are looking for a checkmate or if you are down for a rook isn't enough take a bishop.

Next, look the position of the kings. you need see if can you mate your opponent or him can mate you.

and in third place check the pieces that can be captured.

and the most important when you are doing the firsts problems is do it right! take all the neccesary time you need because understand the basic patterns is the most important.

I think it's best to survrey the position in a number of stages. Firstly, a quick glance to identify board texture, material, and certain "signals/defiencies" in either camp; such as king safety, piece alignment, knight fork distance, hanging pieces, lack of defence/ poor piece co-ordination, etc. The presence of one or more of these features implies there is a tactical motif lurking beneath the surface.

Further analysis identifies critical defenders, weak squares, and speculates on possible tactical motifs. Finally, a few candidate moves are compiled, and calculated starting with the most forcing.

locking opponent's piece to make it unoperable (this works like winning material because the opponent is not able to use the locked piece)

getting other kinds of positional advantage (e.g. if there are more open diagonal in the position than open files a bishop is stronger than a rook so it can be a good choice to sac exchange)

getting unstoppable passer

transposing to drawish endgame (if the current position is worse; the most spectacular example is coming to a stalemate from a completely lost game) or to an endgame with more winning possibilities

All the above require both tactical eye and good positional skills. They are much harder to play as compared to "pure" tactics because the outcome mainly depends on precise assessment of the resulting position.

While we can be sure about a checkmate or perpetual check or winning material we frequently have doubts about the results of a positional combination which ends up with material imbalance. The top grandmasters can sometimes sacrifice a queen for purely positional reasons which the amateurs are not able to understand. Playing such strategical tactics is the sign of highest chess level.

Well, when it comes to "pure" ("normal") tactics proper judgement of the position is also important. If we find a combination which gives perpetual check we should not play it when our position is currently better and gives chances for a win (though it may be reasonable to finish a game in this way when a draw gives clear first place in a tournament - this is also a strategical combination but in sense of tournament strategy not the chess one )

As others pointed out patterns are extremely useful to find tactics. When you are familiar with lots of them you can sometimes find tactical motives by just glancing at the position.

Last but not least - in a game you can help your tactics. When pondering on the current position I frequently examine possible motives which I could use after some moves. I try to figure out which are the factors that currently prevent those tactics (too much defenders on a square, intermezzos, pins etc.) and try to eliminate those obstacles.

If I cannot do anything to enable the tactics I just play normal positional game. However when my opponent blunders it is much easier to exploit the weak move if it has just make one of the previously recognized tactical motives work.